Unraveling the mathematical euphoria of N = 2³+3³+4³+5³+6³+7³+8³+9³
Continue reading “Joyful Cubes!”Unlocking the Fraction
Use a trick to quickly and effortlessly determine the fraction that falls between 3/4 and 4/5.
Math & Art
In 1895, Nicholas Bogdanov-Belsky created the iconic painting “Mental Arithmetic in the Public School of S. Rachinsky,” now a classic. Students are depicted trying to solve the problem on the blackboard: (10²+11²+12²+13²+14²)/365. They seem to be having a great time!
A Curious Constant
A palindromic number is an integer that remains the same when its digits are reversed. The sum of the reciprocals of all the palindromic numbers in the world converges to approximately 3.3703…
Summation Formulas
Some remarkable summation formulas…
φibonacci formula
Because Fn→ φⁿ when n→ ∞
When matrices meet Fibonacci
F0 = 1, F1 = 1, Fn = 1, Fn = Fn-1+ Fn-2, n ≥ 2
Read more: https://mathworld.wolfram.com/FibonacciQ-Matrix.html
Perfect “Square” Circle
Numbers 1 to 32 are placed along the circumference of a circle without repeating any number and still the sum of any two adjacent numbers in this circle is a perfect square!
Sum of Consecutive Cubes (Visual Proof)
The sum of the first n cubes is the square of the nth triangular number:
13 + 23 + 33 + 43 + 53 + . . . + n3 = (1 + 2 + 3 + 4 + 5 + . . . + n)2.
Inverse Powers of Phi
Summation of Alternating Inverse Powers of Phi…